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Approximation of CDF of Non-Central Chi-Square Distribution by Mean-Value Theorems for Integrals

Author

Listed:
  • Árpád Baricz

    (Department of Economics, Babeş-Bolyai University, 400591 Cluj-Napoca, Romania
    Institute of Applied Mathematics, Óbuda University, Bécsi út 96/b, 1034 Budapest, Hungary)

  • Dragana Jankov Maširević

    (Department of Mathematics, University of Osijek, Trg Lj. Gaja 6, 31000 Osijek, Croatia)

  • Tibor K. Pogány

    (Institute of Applied Mathematics, Óbuda University, Bécsi út 96/b, 1034 Budapest, Hungary
    Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000 Rijeka, Croatia)

Abstract

The cumulative distribution function of the non-central chi-square distribution χ n ′ 2 ( λ ) of n degrees of freedom possesses an integral representation. Here we rewrite this integral in terms of a lower incomplete gamma function applying two of the second mean-value theorems for definite integrals, which are of Bonnet type and Okamura’s variant of the du Bois–Reymond theorem. Related results are exposed concerning the small argument cases in cumulative distribution function (CDF) and their asymptotic behavior near the origin.

Suggested Citation

  • Árpád Baricz & Dragana Jankov Maširević & Tibor K. Pogány, 2021. "Approximation of CDF of Non-Central Chi-Square Distribution by Mean-Value Theorems for Integrals," Mathematics, MDPI, vol. 9(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:129-:d:477294
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    References listed on IDEAS

    as
    1. Robert, Christian, 1990. "Modified Bessel functions and their applications in probability and statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 155-161, February.
    2. Unknown, 1976. "Table of Contents," 1976 Symposium, Food and Population: Priorities in Decision Making, August 1976, Nairobi, Kenya 183452, International Association of Agricultural Economists.
    3. Unknown, 1976. "Table of Contents," 1976 Conference, July 26-August 4, 1976, Nairobi, Kenya 274772, International Association of Agricultural Economists.
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